We use signal detection and estimation and simulation methods to optimize the collimator in SPECT (Single Photon Emission Computed Tomography) medical imaging systems. A SPECT system images a radiopharmaceutical in the body to produce raw data called the sinogram that is then reconstructed to form a viewable image. The important imaging component is the collimator which controls a noise/resolution tradeoff in the sinogram. A signal like a tumor can be lost in the blur and noise of the sinogram. We apply an ideal observer to the sinogram to find the best collimator. We address two tasks (1) detect and localize a single signal; (2) detect and localize multiple signals. Task performance of the ideal observer is measured as area under the LROC (Location Receiver Operating Characteristic) curve for task (1), and area under the AFROC (Alternative free response ROC) curve for task (2). In general, we show that low efficiency collimators that yield blurry images with low relative noise outperform conventional clinical collimators that yield higher resolution but noisier images.